Timings and memory consumption for the singular value decomposition implemented in scipy. The script svd_memory.py generates a plot about the memory consumption (requires the package `memory_profiler`) and the second one will plot the timings. The scripts will perform several iterations for matrices of different sizes and will take about 30 minu…

svd_memory.py

# .. Memory benchmarks for SciPy's Singular Value Decomposition ..
# .. Author: Fabian Pedregosa <[email protected]>

import numpy as np
from scipy.sparse import linalg as splinalg
from scipy import sparse, linalg
import pylab as pl
from memory_profiler import memory_usage

dims = np.arange(500, 1500, 20)
n_iter = 3
LAPACK_mem = np.zeros((n_iter, dims.size))
ARPACK_mem = np.zeros((n_iter, dims.size))

for i_iter in range(n_iter):
    for i_dim, k in enumerate(dims):
        x = np.random.randn(k, k)
        tmp = memory_usage((linalg.svd, (x,)))
        LAPACK_mem[i_iter, i_dim] = np.max(tmp)
        tmp = memory_usage((splinalg.svds, (x,)))
        ARPACK_mem[i_iter, i_dim] = np.max(tmp)


def errorfill(x, y, yerr, color=None, alpha_fill=0.3, ax=None, label=None):
    # helper function, stolen from http://tonysyu.github.com/plotting-error-bars.html
    ax = ax if ax is not None else pl.gca()
    if color is None:
        color = ax._get_lines.color_cycle.next()
    if np.isscalar(yerr) or len(yerr) == len(y):
        ymin = y - yerr
        ymax = y + yerr
    elif len(yerr) == 2:
        ymin, ymax = yerr
    ax.plot(x, y, color=color, label=label)
    ax.fill_between(x, ymax, ymin, color=color, alpha=alpha_fill)

errorfill(dims, LAPACK_mem.mean(0), LAPACK_mem.std(0), label='linalg.svd')
errorfill(dims, ARPACK_mem.mean(0), ARPACK_mem.std(0), label='sparse.linalg.svds')
pl.ylabel('Memory (in MB)')
pl.legend(loc='upper left')
pl.axis('tight')
pl.show()

svd_timing.py

# .. Benchmarks for SciPy's Singular Value Decomposition ..
# .. Author: Fabian Pedregosa <[email protected]>

import time
import numpy as np
from scipy.sparse import linalg as splinalg
from scipy import sparse, linalg
import pylab as pl

dims = np.arange(500, 1500, 20)
n_iter = 3
LAPACK_time = np.zeros((n_iter, dims.size))
ARPACK_time = np.zeros((n_iter, dims.size))

# .. we perform several runs for greater stability ..
for i_iter in range(n_iter):
    for i_dim, k in enumerate(dims):
        # .. create the data ..
        x = np.random.randn(k, k)
        t0 = time.time()
        linalg.svd(x)
        LAPACK_time[i_iter, i_dim] = time.time() - t0
        t0 = time.time()
        splinalg.svds(x, k-1)
        ARPACK_time[i_iter, i_dim] = time.time() - t0


# .. plot the result .. 

def errorfill(x, y, yerr, color=None, alpha_fill=0.3, ax=None, label=None):
    # helper function, stolen from http://tonysyu.github.com/plotting-error-bars.html
    ax = ax if ax is not None else pl.gca()
    if color is None:
        color = ax._get_lines.color_cycle.next()
    if np.isscalar(yerr) or len(yerr) == len(y):
        ymin = y - yerr
        ymax = y + yerr
    elif len(yerr) == 2:
        ymin, ymax = yerr
    ax.plot(x, y, color=color, label=label)
    ax.fill_between(x, ymax, ymin, color=color, alpha=alpha_fill)

errorfill(dims, LAPACK_time.sum(0), LAPACK_time.std(0),  label='linalg.svd')
errorfill(dims, ARPACK_time.sum(0), LAPACK_time.std(0), label='sparse.linalg.svds')
pl.ylabel('Time (in seconds)')
pl.xlabel('Size of matrices')
pl.legend(loc='upper left')
pl.axis('tight')
# pl.savefig('svd_timing.png')
pl.show()